The derivation of the nonlinear, dispersive Boussinesq equations under discussion deviates from the work done in the literature, even when the same assumptions and approximations have been employed.

Six local and seven non local conservation laws for the (1+1)$(1+1)$D linearized Boussinesq equations are obtained.

Four conserved quantities are obtained using a systematic multiplier approach with four conserved densities matching existing classical wave theory literature.

One of these conserved quantities has not been directly commented on in the literature and relates to an energy flux density.

A new conserved density is obtained which we as yet cannot relate to any known physical quantities.